Self-trapping of light using the Pancharatnam-Berry phase

Since its introduction by Berry in 1984, the geometric phase has become of fundamental importance in physics, with applications ranging from solid-state physics to optics. In optics, the Pancharatnam-Berry phase allows the tailoring of optical beams by a local control of their polarization. Here, we discuss light propagation in the presence of an intensity-dependent local modulation of the Pancharatnam-Berry phase. The corresponding self-modulation of the wave front counteracts the natural spreading due to diffraction; i.e., self-focusing takes place. No refractive index variation is associated with the self-focusing: The confinement is uniquely due to a nonlinear spin-orbit interaction. The phenomenon is investigated, both theoretically and experimentally, by considering the reorientational nonlinearity in liquid crystals, where light is able to rotate the local optical axis through an intensity-dependent optical torque. Our discoveries pave the way to the investigation of a new family of nonlinear waves featuring a strong interaction between the spin and the orbital degrees of freedom